Answer
\[3-5\ln|t+1|+C\]
Work Step by Step
Let \[I=\int\frac{3t-2}{t+1}dt\]
\[I=\int\frac{3(t+1)-5}{t+1}dt\]
\[I=\int\left(3-\frac{5}{t+1}\right)dt\]
\[I=3-5\ln|t+1|+C\]
Where $C$ is constant of integration
Hence $\;\;I=3-5\ln|t+1|+C$.
Calculus 8th Edition
by Stewart, James
Published by
Cengage
ISBN 10:
1285740629
ISBN 13:
978-1-28574-062-1
Chapter 7 - Techniques of Integration - 7.4 Integration of Rational Functions by Partial Fractions - 7.4 Exercises - Page 541: 8
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